David Mumford

Archive for Reprints, Notes, Talks, and Blog

Professor Emeritus
Brown and Harvard Universities
David_Mumford@brown.edu

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Work on Moduli and Geometric Invariant Theory (except Abelian Varieties)

Moduli spaces are essentially maps. In an ordinary map, a point on a piece of paper corresponds to a location on the earth. Similarly, a point in a moduli space corresponds to an object of some kind, a variety or bundle or something more elaborate. The set of all these objects is thus put together in this fine but rather intangible 'map' known as a moduli space. That's why I have put a map of part of Maine in the background.

  • An Elementary theorem in Geometric Invariant Theory, Bull. Amer. Math. Soc., 1961, pp. 483-487. Scanned reprint and DASH reprint
  • Topics in the Theory of Moduli, (published in Japanese), Sugaku , 1963. Scanned English manuscript
  • Projective Invariants of Projective Structures, International Congress of Mathematicians, Stockholm 1962, 1963, pp. 526-530. Scanned reprint
  • The Boundary of Moduli Schemes, mimeographed notes from the 1964 Woods Hole Symposium on Algebraic Geometry. Scanned manuscript
  • Picard Groups of Moduli Problems, in Arithmetic Algebraic Geometry, (Proceedings of a Conference in Purdue, 1963), Harper and Row, 1965. Scanned reprint
  • Two Fundamental Theorem on Deformations of Polarized Varieties (with T. Matsusaka), Amer. J. of Math., 1964, pp. 668-684. Scanned reprint and DASH reprint
  • Cover of the book Geometric Invariant Theory, Springer-Verlag, 1965; 2nd enlarged edition, (with John Fogarty), 1982; 3rd enlarged edition, (with Frances Kirwan and John Fogarty), 1994, DejaVu
  • Abelian Quotients of the Teichmuller Modular Group, Journal d'Analyse, 1967, 28, pp. 227-244. Scanned reprint
  • Periods of Moduli Spaces of Bundles on Curves (with P. Newstead), Amer. J. of Math., 1968, 90, pp. 1200-1208. Scanned reprint and DASH reprint
  • The Irreducibility of the Space of Curves of Given Genus (with P. Deligne), Publ. Math. de l'I.H.E.S., 1969, 36, pp. 75-109. Scanned reprint and DASH reprint
  • A Remark on Mahler's Compactness Theorem, Proc. Amer. Math. Soc., 1971, 28, pp. 289-194. Scanned reprint and DASH reprint
  • The Structure of the Moduli Spaces of Curves and Abelian Varieties, Actes du Congress Int. du Math., Nice, 1970; Gauthier-Villars, 1971. Scanned reprint
  • Introduction to the Theory of Moduli (with K. Suominen), in Algebraic Geometry, Oslo 1970 F. Oort editor, Wolters-Noordhoff, 1972, pp. 171-222.Scanned reprint
  • Matsusaka's Big Theorem (with D. Lieberman), in Algebraic Geometry, Arcata 1974, AMS Proc. of Symposia in Pure Math., 29, 1975, pp. 513-530. Scanned reprint
  • The projectivity of the moduli space of stable curves, I: Preliminaries on "det" and "Div" (with F. Knudsen), Math. Scand., 39, 1976, pp.19-55.
    The projectivity of the moduli space of stable curves, II: the stacks Mg,n (sequel by F. Knudsen), Math. Scand., 52, 1983, pp.161-199.
    The projectivity of the moduli space of stable curves III: the line bundles on Mg,n and a proof of trhe projectivity of the completion of Mg,n in characteristic 0 (sequel by F. Knudsen), Math. Scand., 52, 1983, pp.200-212. Scanned reprint
  • Stability of Projective Varieties, Monographie No. 24 de L'Enseignement Math., 23, 1977, pp. 39-110. Scanned reprint
  • On the Kodaira Dimension of the Moduli Space of Curves (with Joe Harris and an appendix by William Fulton), Inv. Math., 1982, pp.23-88. Scanned reprint and DASH reprint
  • Towards an Enumerative Geometry of Moduli Space of Curves, in Arithmetic and Geometry, edited by M. Artin, J. Tate, Birkhauser-Boston, 1983, pp.271-326. Scanned reprint
  • A Stratification of the Null Cone via the Moment Map (with Linda Ness), Amer. J. of Math., 106, 1984, pp.1281-1329. Scanned reprint and DASH reprint